PCA and Naive Bayes Classifier - python

I'm experimenting with PCA and Naive Bayes Classifier in Python.
In short, using a database of gray-scale images of digits, I'm reducing dimensions with PCA and then using Naive Bayes to classify.
I use 2,4,10,30,60,200,500,784 components respectively.
The classification error rates I get respectively are:
0.25806452, 0.15322581, 0.06290323, 0.06451613, 0.06451613, 0.10322581, 0.28064516 and 0.31774194. I thought that taking more components always improved the accuracy of classification. Is this true? If so then I am doing something wrong.

I don't think there is a single valid answer to your question, but reducing the dimensionality of your input can prevent overfitting. More features does not always make your classifier more accurate. You can look here for a detailed explanation: http://www.visiondummy.com/2014/04/curse-dimensionality-affect-classification/

It is true that reducing dimensions reduces overfitting, but there is always an optimal number of components which gives the best accuracy if you are not adding additional data to the dataset. In your case, it is 10 since it gives the least error rate of 0.06290323. So, if you are increasing dimensionality you should also increase the dataset for training in order to expect more accuracy. Otherwise, You should try a Grid search near it for more accuracy.
Also if your dataset is balanced then accuracy may be a good measure of evaluating your performance. In case of imbalanced dataset try Precision, Recall or f-score .
If still, you are not satisfied with the classifier use some other classification algorithm.

Related

Identical accuracy in different ML Classification models

I used the "Stroke" data set from kaggle to compare the accuracy of the following different models of classification:
K-Nearest-Neighbor (KNN).
Decision Trees.
Adaboost.
Logistic Regression.
I did not implement the models myself, but used sklearn library's implementations.
After training the models I ran the test data and printed the level of accuracy of each of the models and these are the results:
As you can see, KNN, Adaboost, and Logistic Regression gave me the exact same accuracy.
My question is, does it make sense that there is not even a small difference between them or did I make a mistake somewhere along the way (Even though I only used sklearn's implementations?
In general achieving the same scores is unlikely, and the explanation is usually:
bug in actual reporting
bug in the data processing
score reported corresponds to a degenerate solution
And the last explanation is probably the case. Stroke dataset has 249 positive samples in 5000 datapoints, so if your model always says "no stroke" it will get roughly 95%. So my best guess is that all your models failed to learn anything and are just constantly outputting "0".
In general accuracy is not a right metric for highly imabalnced datasets. Consider balanced accuracy, f1, etc.

How to check machine learning accuracy without cross validation

I have training sample X_train, and Y_train to train and X_estimated.
I got task to make my classificator learn as accurate as it can, and then predict vector of results over X_estimated to get close results to Y_estimated (which i have now, and I have to be as much precise as it can). If I split my training data to like 75/25 to train and test it, I can get accuracy using sklearn.metrics.accuracy_score and confusion matrix. But I am losing that 25% of samples, that would make my predictions more accurate.
Is there any way, I could learn by using 100% of the data, and still be able to see accuracy score (or percentage), so I can predict it many times, and save best (%) result?
I am using random forest with 500 estimators, and usually get like 90% accuracy. I want to save best prediction vector as possible for my task, without splitting any data (not wasting anything), but still be able to calculate accuracy (so I can save best prediction vector) from multiple attempts (random forest always shows different results)
Thank you
Splitting your data is critical for evaluation.
There is no way that you could train your model on 100% of the data and be able to get a correct evaluation accuracy unless you expand your dataset. I mean, you could change your train/test split, or try to optimize your model in other ways, but i guess the simple answer to your question would be no.
As per your requirement, you can try K Fold Cross Validation. If you split it in 90|10 i.e for Train|Test. Achieving to take 100% data for training is not possible as you have to test the data then only you can validate the same that how good your model is. K Fold CV takes your whole train data into consideration in each fold and randomly takes test data sample from the train data. And lastly calculates the accuracy by taking summation of all the folds. Then finally you can test the accuracy by using 10% of the data.
More you can read here and here
K Fold Cross Validation
Skearn provides simple methods for performing K fold cross validation. Simply you have to pass no of folds in the method. But then remember, more the folds, it takes more time to train the model. More you can check here
It is not necessary to do 75|25 split of your data all the time. 75
|25 is kind of old school now. It greatly depends on the amount of data that you have. For example, if you have 1 billion sentences for training a language model, it is not necessary to reserve 25% for testing.
Also, I second the previous answer of trying K-fold cross-validation. As a side note, you could consider looking at the other metrics like precision and recall as well.
In general splitting your data set is critical for evaluation. So I would recommend you always do that.
Said that, there are methods that in some sense allow you to train on all your data and still get an estimate of your performance or to estimate the generalization accuracy.
One particularly prominent method is leveraging out-of-bag samples of models based on bootstrapping, i.e. RandomForests.
from sklearn.ensemble import RandomForestClassifier
rf = RandomForestClassifier(n_estimators=100, bootstrap=True, oob_score=True)
rf.fit(X, y)
print(rf.oob_score_)
if you are doing classification always go with stratified k-fold cv(https://machinelearningmastery.com/cross-validation-for-imbalanced-classification/).
if you're doing regression then go with simple k-fold cv or you can divide the target as bins and do stratified k-fold cv. by this way you can use your data completely in model training.

Using Precision and Recall in training of skewed dataset

I have a skewed dataset (5,000,000 positive examples and only 8000 negative [binary classified]) and thus, I know, accuracy is not a useful model evaluation metric. I know how to calculate precision and recall mathematically but I am unsure how to implement them in python code.
When I train the model on all the data I get 99% accuracy overall but 0% accuracy on the negative examples (ie. classifying everything as positive).
I have built my current model in Pytorch with the criterion = nn.CrossEntropyLoss() and optimiser = optim.Adam().
So, my question is, how do I implement precision and recall into my training to produce the best model possible?
Thanks in advance
The implementation of precision, recall and F1 score and other metrics are usually imported from the scikit-learn library in python.
link: http://scikit-learn.org/stable/modules/classes.html#module-sklearn.metrics
Regarding your classification task, the number of positive training samples simply eclipse the negative samples. Try training with reduced number of positive samples or generating more negative samples. I am not sure deep neural networks could provide you with an optimal result considering the class skewness.
Negative samples can be generated using the Synthetic Minority Over-sampling Technique (SMOT) technique. This link is a good place to start.
Link: https://www.analyticsvidhya.com/blog/2017/03/imbalanced-classification-problem/
Try using simple models such as logistic regression or random forest first and check if there is any improvement in the F1 score of the model.
To add to the other answer, some classifiers have a parameter called class_weight which let's you modify the loss function. By penalizing wrong predictions on the minority class more, you can train your classifier to learn to predict both classes.
For a pytorch specific answer, you can refer this link
As mentioned in the other answer, over and undersampling strategies can be used. If you are looking for something better, take a look at this paper

What are good metrics to evaluate the performance of a multi-class classifier?

I'm trying to run a classifier in a set of about 1000 objects, each with 6 floating point variables. I've used scikit-learn's cross validation features to generate an array of the predicted values for several different models. I've then used sklearn.metrics to compute the accuracy of my classifiers, and the confusion table. Most classifiers have around 20-30% accuracy. Below is the confusion table for the SVC classifier (25.4% accuracy).
Since I'm new to machine learning, I'm not sure how to interpret that result, and whether there are other good metrics to evaluate the problem. Intuitively speaking, even with 25% accuracy, and given that the classifier got 25% of the predictions right, I believe it is at least somewhat effective, right? How can I express that with statistical arguments?
If this table is a confusion table, I think that your classifier predicts in majority of the time the class E. I think that your class E is overrepresented in your dataset, accuracy is not a good metric if your classes have not the same number of instances,
Example, If you have 3 classes, A,B,C and in the test dataset the class A is over represented (90%) if your classifier predicts all time class A, you will have 90% of accuracy,
A good metric is to use log loss, logistic regression is a good algorithm that optimize this metric
see https://stats.stackexchange.com/questions/113301/multi-class-logarithmic-loss-function-per-class
An other solution, is to do oversampling of your small classes
First of all, I find it very difficult to look at confusion tables. Plotting it as an image would give a lot better intuitive understanding about what is going on.
It is advisory to have single number metric to optimize since it is easier and faster. When you find that your system doesn't perform as you expect it to, revise your selection of metric.
Accuracy is usually a good metric to use if you have same amount of examples in every class. Otherwise (which seems to be the case here) I'd advise to use F1 score which takes into account both precision and recall of your estimator.
EDIT: However it is up to you to decide if the ~25% accuracy, or whatever metric is "good enough". If you are classifying if robot should shoot a person you should probably revise your algorithm but if you are deciding if it is a pseudo-random or random data, 25% percent accuracy could be more than enough to prove the point.

When using multiple classifiers - How to measure the ensemble's performance? [SciKit Learn]

I have a classification problem (predicting whether a sequence belongs to a class or not), for which I decided to use multiple classification methods, in order to help filter out the false positives.
(The problem is in bioinformatics - classifying protein sequences as being Neuropeptide precursors sequences. Here's the original article if anyone's interested, and the code used to generate features and to train a single predictor) .
Now, the classifiers have roughly similar performance metrics (83-94% accuracy/precision/etc' on the training set for 10-fold CV), so my 'naive' approach was to simply use multiple classifiers (Random Forests, ExtraTrees, SVM (Linear kernel), SVM (RBF kernel) and GRB) , and to use a simple majority vote.
MY question is:
How can I get the performance metrics for the different classifiers and/or their votes predictions?
That is, I want to see if using the multiple classifiers improves my performance at all, or which combination of them does.
My intuition is maybe to use the ROC score, but I don't know how to "combine" the results and to get it from a combination of classifiers. (That is, to see what the ROC curve is just for each classifier alone [already known], then to see the ROC curve or AUC for the training data using combinations of classifiers).
(I currently filter the predictions using "predict probabilities" with the Random Forests and ExtraTrees methods, then I filter arbitrarily for results with a predicted score below '0.85'. An additional layer of filtering is "how many classifiers agree on this protein's positive classification").
Thank you very much!!
(The website implementation, where we're using the multiple classifiers - http://neuropid.cs.huji.ac.il/ )
The whole shebang is implemented using SciKit learn and python. Citations and all!)
To evaluate the performance of the ensemble, simply follow the same approach as you would normally. However, you will want to get the 10 fold data set partitions first, and for each fold, train all of your ensemble on that same fold, measure the accuracy, rinse and repeat with the other folds and then compute the accuracy of the ensemble. So the key difference is to not train the individual algorithms using k fold cross-validation when evaluating the ensemble. The important thing is not to let the ensemble see the test data either directly or by letting one of it's algorithms see the test data.
Note also that RF and Extra Trees are already ensemble algorithms in their own right.
An alternative approach (again making sure the ensemble approach) is to take the probabilities and \ or labels output by your classifiers, and feed them into another classifier (say a DT, RF, SVM, or whatever) that produces a prediction by combining the best guesses from these other classifiers. This is termed "Stacking"
You can use a linear regression for stacking. For each 10-fold, you can split the data with:
8 training sets
1 validation set
1 test set
Optimise the hyper-parameters for each algorithm using the training set and validation set, then stack yours predictions by using a linear regression - or a logistic regression - over the validation set. Your final model will be p = a_o + a_1 p_1 + … + a_k p_K, where K is the number of classifier, p_k is the probability given by model k and a_k is the weight of the model k. You can also directly use the predicted outcomes, if the model doesn't give you probabilities.
If yours models are the same, you can optimise for the parameters of the models and the weights in the same time.
If you have obvious differences, you can do different bins with different parameters for each. For example one bin could be short sequences and the other long sequences. Or different type of proteins.
You can use the metric whatever metric you want, as long as it makes sens, like for not blended algorithms.
You may want to look at the 2007 Belkor solution of the Netflix challenges, section Blending. In 2008 and 2009 they used more advances technics, it may also be interesting for you.

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